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The cost C, in dollars of producing x units of a certain commodity is

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The cost C, in dollars of producing x units of a certain commodity is [#permalink]

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New post Updated on: 24 Apr 2016, 11:36
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The cost C, in dollars of producing x units of a certain commodity is given by the formula C(x) = 10.000 + bx + ax^2 where a, and b are constants. What is the value of a?

(1) The cost of producing 500 units is $15.833.

(2) The cost of producing 1,000 units is twice the cost of producing 500 units.

Originally posted by inakihernandez on 24 Apr 2016, 10:20.
Last edited by Vyshak on 24 Apr 2016, 11:36, edited 1 time in total.
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Re: The cost C, in dollars of producing x units of a certain commodity is [#permalink]

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New post 24 Apr 2016, 10:58
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inakihernandez wrote:
The cost C, in dollars of producing x units of a certain commodity is given by the formula C(x) = 10.000 + bx + ax^2 where a, and b are constants. What is the value of a?

(1) The cost of producing 500 units is $15.833.

(2) The cost of producing 1,000 units is twice the cost of producing 500 units.


Hi
the equation has got two constants a and b..

lets see the statements



(1) The cost of producing 500 units is $15.833.
we have two constants a and b, and one equation
Insuff

(2) The cost of producing 1,000 units is twice the cost of producing 500 units
here when you make two quation and equate them you will realize you can find answer..
C(1000) = 10.000 + b*1000 + a1000^2 ..
C(500) = 10.000 + b*500 + a500^2 ..

now C(1000) = 2* C(500)..
so 10.000 + b*1000 + a1000^2 = 2( 10.000 + b*500 + a500^2 )..
10.000 + b*1000 + a1000^2 = 20.000 + b*1000 + 2*a*500^2
b will get cancelled and you can find value of a..
Suff

Hope it helps
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Re: The cost C, in dollars of producing x units of a certain commodity is [#permalink]

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New post 24 Apr 2016, 10:47
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Hi inakihernandez,

You should post this question in the DS sub-Forum here:

gmat-data-sufficiency-ds-141/

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Re: The cost C, in dollars of producing x units of a certain commodity is [#permalink]

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New post 24 Apr 2016, 11:02
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C(x) = 10.000 + bx + ax^2
a = ?

St1: C(500) = 10 + 500b + a(25*10^4 ) = 15.833
We have 2 unknowns and hence value of 'a' cannot be determined without knowing the value of 'b'
Not Sufficient

St2: C(1000) = 2*C(500)
10 + 1000b + a(10^6) = 20 + 1000b + a(50*10^4)
a(10^6 - 5*10^5) = 10
Sufficient to determine the value of 'a'

Answer: B
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Re: The cost C, in dollars of producing x units of a certain commodity is [#permalink]

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New post 24 Apr 2016, 11:10
1
Vyshak wrote:
C(x) = 10.000 + bx + ax^2
a = ?

St1: C(500) = 10 + 500b + a(25*10^4 ) = 15.833
We have 2 unknowns and hence value of 'a' cannot be determined without knowing the value of 'b'
Not Sufficient

St2: C(1000) = 2*C(500)
10 + 1000b + a(10^6) = 20 + 1000b + a(50*10^4)
a(10^6 - 5*10^5) = 10
Sufficient to determine the value of 'a'

Answer: B


how did you get this?
a(25*10^4 )
a(50*10^4)
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Re: The cost C, in dollars of producing x units of a certain commodity is [#permalink]

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New post 24 Apr 2016, 11:13
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paidlukkha wrote:
Vyshak wrote:
C(x) = 10.000 + bx + ax^2
a = ?

St1: C(500) = 10 + 500b + a(25*10^4 ) = 15.833
We have 2 unknowns and hence value of 'a' cannot be determined without knowing the value of 'b'
Not Sufficient

St2: C(1000) = 2*C(500)
10 + 1000b + a(10^6) = 20 + 1000b + a(50*10^4)
a(10^6 - 5*10^5) = 10
Sufficient to determine the value of 'a'

Answer: B


how did you get this?
a(25*10^4 )
a(50*10^4)


Hi,

I have skipped some multiplication steps in my explanation.

x = 5*10^2 --> x^2 = 25*10^4

2*C(500) --> 2(10 + 500b + 25*10^4) --> 20 + 1000b + 2*25*10^4
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Re: The cost C, in dollars of producing x units of a certain commodity is [#permalink]

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New post 24 Apr 2016, 21:04
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inakihernandez wrote:
The cost C, in dollars of producing x units of a certain commodity is given by the formula C(x) = 10.000 + bx + ax^2 where a, and b are constants. What is the value of a?

(1) The cost of producing 500 units is $15.833.

(2) The cost of producing 1,000 units is twice the cost of producing 500 units.


Let me point out here that this is a (C) trap question. The first statement will give an equation in a and b. So we know that we cannot find the value of a. When we look at the second statement, we see another equation in a and b which is not a multiple of the first equation and suddenly, it seems that we will be able to solve both equations simultaneously and get the answer. So (C) seems to be correct. But that is just too easy. Beware of the (C) trap. This should make you think - can I solve the question using a single statement alone. Make the equation of statement 2 since it gives you some convoluted relative data. When you do, you see that b gets canceled and in fact, you can get the value of a. Note that you cannot find the value of b from the second statement alone but the question doesn't ask for the value of b. We only need the value of a and hence second statement is sufficient alone.
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Re: The cost C, in dollars of producing x units of a certain commodity is [#permalink]

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New post 09 Oct 2016, 04:29
The correct statement 1 is
(1) The cost of producing 500 units of this commodity is $15833

It is NOT 15.833 although that won't affect the OA.
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Re: The cost C, in dollars of producing x units of a certain commodity is [#permalink]

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Re: The cost C, in dollars of producing x units of a certain commodity is   [#permalink] 09 Oct 2017, 06:44
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